In [1]} light was injected in a corner of the ensemble of modulated wave guides and light was observed coming out at the opposite corner. It was inferred that their observation is equivalent to adiabatic pumping along the cycle mapped in Fig. REF (h) (see also [2]}). We were indeed able to reproduce this interesting corner-to-corner pumping effect (see Supplementary Material), but let us point out that this type of pumping occurs through the bulk states. In an actual pumping experiment, this will inherently lead to leakage into the bulk modes. The Weyl singularity, however, gives access to additional pumping cycles that avoid the bulk spectrum. Indeed, one of the special features of a strong topological invariant, such as the 2nd Chern number, is that boundary modes occur regardless of the orientation of the boundary. This feature, together with the full control over the phason, enable a corner-to-corner mode steering that does not proceed through the bulk states but rather goes around the Weyl singularity, as well as around the edges of the sample. The effect is illustrated in Fig. REF , were a section of the Weyl singularity was sampled at eight points in Fig. REF (b) and the spatial profiles of the corresponding eigenmodes were mapped in Fig. REF (c). As one can see, the mode is steered around the boundary of the crystal and completes a full cycle as the phason is cycled over the section of the Weyl singularity.
